Cooperative Transmission for Underwater Acoustic Communications

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Cooperative transmission is a new wireless communication technique in which ... significant advantage over the traditional direct transmission and over the ...
Cooperative Transmission for Underwater Acoustic Communications

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Zhu Han and Yan Lindsay Sun+ Electrical and Computer Engineering Department, Boise State University, Boise, ID, USA + Department of Electrical and Computer Engineering, University of Rhode Island, Rhode Island, USA Abstract—Underwater acoustic channel usually has low data rate, long propagation delay, severe multipath effect, and time varying fading. Cooperative transmission is a new wireless communication technique in which diversity gain is achieved by utilizing relay nodes as virtual antennas. In this paper, we investigate cooperative transmission techniques for underwater acoustic communications. First, we study the performance of several cooperative transmission schemes, originally designed for radio communications, in the underwater scenario. Second, taking advantage of the low propagation speed of sound, we design a new wave cooperative transmission scheme. In this scheme, the relay nodes amplify the signal received from the source node, and then forward the signal immediately to the destination. The goal is to influence the multipath effect at the receiver. Third, we derive a performance upper bound for the proposed wave cooperative transmission scheme. The simulation results show that the proposed wave cooperative transmission has significant advantage over the traditional direct transmission and over the existing cooperative transmission schemes that are originally designed for radio wireless networks.

I. I NTRODUCTION Underwater acoustic communication techniques [1]–[5] are critical to a number of applications. Most early underwater acoustic systems are established for military applications. Recently, there is an increasing interest in building civilian underwater networks. Without relying on wires, acoustic networks are easy to deploy and present low hazard to surrounding moving objects. Typical civilian applications of underwater networks include oil prospecting search and recovery, drown detection, tsunami alarming, underwater habitat, and pollution monitoring, etc. Sound can travel longer distance in water than electromagnetive wave. However, underwater acoustic communication channels normally have limited bandwidth and high level of reverberation that can cause severe signal dispersion in both time and frequency domains. Sound wave experiences frequency-related attenuation caused by absorption and scattering. The propagation can be refracted by gradient of water conditions. Rays of sound from the same emitter arrive at the receiver through various paths depending upon their launching angles. Travel times along these paths can be significantly different because the speed of sound is several orders lower than that of light. Scattered sound waves from various scatters and geographic boundaries bring in additional challenges for signal reception. Furthermore, time-varying propagation happens due to the Doppler effect resulting from sea surface motion and source/receiver movement. Underwater communication systems have evolved from analog to digital and from incoherent to coherent. Researchers and developers have improved the system to achieve larger bandwidth for practical usage. Demonstrated results include 1kbps at 90km, 100kbps at 0.1km, and 500kbps at 60m [5]. Underwater acoustic communications are rapidly growing [6]–[8] motivated by the

increasing demand on exploiting underwater environment. It is necessary to further improve the transmission rate and reliability in underwater acoustic communications. Recently, cooperative transmission [9]–[12] has gained a considerable amount of attention as a transmit strategy for future wireless networks. The basic idea of cooperative transmission is that the relay nodes can help the source node’s transmission by sending a replica of the source’s information. Cooperative communication takes advantage of the broadcast nature of wireless media, and exploits the inherent spatial and multiuser diversities. In this paper, we explore the possibility and benefits of utilizing cooperative transmission in the underwater environment. We believe that this technique, new to acoustic communications, can overcome many channel limitations and increase the overall transmission rate of underwater acoustic channels. Three different strategies of cooperative transmission, previously used in wireless communications, are evaluated in the underwater scenario. Moreover, based on the low propagation speed of sound, we propose a wave cooperative transmission in which the relay amplifies the source information when the source wave passes and the destination can receive additional high strength multipath components. We derive a performance upper bound of the proposed scheme. Through simulations, we demonstrate the multipath effects under the influence of cooperative transmission. The proposed wave cooperative transmission has significant advantages over the traditional direct transmission and the other cooperative transmission protocols originally used in the wireless networks. The paper is organized as follows: In Section II, we give the underwater acoustic channel models. In Section III, we describe three cooperative transmission protocols used in wireless communication, and propose the wave cooperative protocol for underwater communications. The performance upper bound is derived and implementation concerns are also discussed in this section. Simulation results are presented in Section IV, and Section V concludes the paper. II. U NDERWATER ACOUSTIC C HANNEL In general, the energy loss during underwater sound propagation is caused by geometric spreading, attenuation, and other path related losses. The attenuation sources can be further categorized into medium absorption and scattering. Among these factors, in a given area, spreading and attenuation caused by absorption are relative stable in a given area. Depending on the spacial boundary of the water, the spreading loss can be modelled as either spherical for deep water or cylindrical for shallow water, corresponding to an inverse-square or inverse first power relation with the propagation range. Attenuation is normally caused by medium absorption and scattering.

The absorption loss between two locations can be described as I2 − I1 = −αd,

(1)

Base station

where I2 and I1 are the intensities in dB at two locations, d is the distance in kilometers between these locations and α is the absorption coefficient in dB per kilometer. The absorption coefficient increases with sound frequency. It is also related to the density of water. Thorp’s formula [1]–[4] approximates the relation as: α=

0.11f 2 44f 2 + + 2.75 × 10−4 f 2 + 0.003 1 + f2 4100 + f 2

Acoustic Direct links

s Underwater sensor nodes

(2)

Acoustic Relay links

caused by sea surface fluctuation, various processes near the sea surface, and source/receiver motion. The source/receiver motion leads to multiple spreading effects. A small change in source and receiver locations can result in interference fluctuation [5], thus can further alter the result from multipath superposition. III. U NDERWATER C OOPERATIVE T RANSMISSION A. Three Cooperative Transmission Protocols Figure 1 illustrates the system structure. It contains a source node s, a relays node r and a destination node d. The cooperative transmission from the source to the destination is accomplished in two phases. In Phase 1, source s broadcasts information through sound wave to both destination d and relay node r. The received signals Yd and Yr at destination d and relay r can be expressed as p Yd = Ps Gs,d X + nd , (5)

(3)

where c1 and c2 are the sound speeds in media 1 and 2, θ1 and θ2 are the grazing angles at the boundary. The value of sound speed depends on three factors: water salinity, temperature, and density. Briefly speaking, sound speed increases with the increment of any one of the above three factors. Several empirical formulae have been proposed by oceanographists. Here we present Coppens equation as an example (refer to [14] for coefficient values) cO,S,T = c0 + c1 T + c2 T 2 + c3 T 3 + (c4 + c5 T + c6 T 2 )(S − 35) cD,S,T = cO,S,T + (c7 + c8 T )D + (c9 + c10 T )D2 +[c11 + c12 (S − 35)] · (S − 35) · T · D,

d

Fig. 1: Underwater acoustic cooperative transmission system

where f is the sound frequency in kilohertz. Sound can be scattered by particles and objects along the propagation path, resulting in energy loss. The amount and locations of scatterers in water can vary from time to time in a given area. Besides random scattering, sound wave is refracted at the boundary of different water conditions. This phenomenon is similar to the case that a light ray bends its path when it travels through different media. The refraction of sound can be calculated using the sound speed of the media. It follows Snell’s law: cos θ1 cos θ2 = , c1 c2

r

and Yr =

(4)

where D is the depth, S is salinity, and T is water temperature. The distribution of sound speed in ocean normally conforms to a general profile. However near shores and estuaries, high gradients of sound speed can occur frequently [4], and thus resulting in irregular acoustic channels. With the knowledge of sound speed distribution and boundary conditions, the transmission loss of sound can be computed by solving the wave equation of the acoustic field. Most numerical solutions of the equation are based on ray theory, normalmode theory, and parabolic equation method. In Section IV we use a method based on the ray theory to calculate the sound transmission loss. In addition to energy loss, underwater sound propagation normally experiences time spreading and the Doppler effects, both of which are important factors for acoustic communication systems at high frequency. The impact of time spreading depends upon the extent of the multipath effect, which in turn is affected by the configuration of a sound channel, i.e. depth of the source/receiver, distance between the source and receiver, and the shape of the ocean floor. The roughness of the sea surface and the sea floor can also lead to time spreading. The Doppler effects can be classified into frequency shifting and frequency spreading. Doppler shifting is induced by source/receiver motion, while Doppler spreading is

p

Ps Gs,r X + nr ,

(6)

where Ps represents the transmit power from source s, X is the transmitted information symbol with unit energy at the source in Phase 1, Gs,d and Gs,r are channel gains from s to d and s to r respectively, nd and nr are the additive white Gaussian noises (AWGN). Without loss of generality, we assume same noise power, σ 2 , for all links. We also assume that channels are stable within each transmission frame. With direct transmission, the signal-to-noise ratio (SNR) of the direct transmission (s -d) can be expressed as Ps Gs,d , σ2 and the information rate of the direct transmission is ¡ ¢ Rs,d = W log2 1 + ΓDT s,d , ΓDT s,d =

(7)

(8)

where W is the bandwidth for information transmission. In Phase 2, the signal is forwarded by a relay node and the receiver uses this additional copy of signal to enhance the reception. The specific way of handling signals varies in different strategies. In the amplify-and-forward (AF) cooperative transmission, the relay node amplifies Yr and forwards it to the destination with transmission power of Pr . The received signal at the destination is p (9) Y2,d = Pr Gr,d Xr + n0d , 2

air

(10)

water

is the transmitted signal from the source to the destination with normalized energy in Phase 1, Gr,d is the channel gain from the relay to the destination, and n0d is the received noise in Phase 2. Substituting (6) into (10), we rewrite (9) as p p Pr Gr,d ( Ps Gs,r Xs + nr ) p Y2,d = + n0d . (11) Ps Gs,r + σ 2

source

Delay profile w/o relay

destination relay

ground

Pr Ps Gr,d Gs,r . = 2 σ (Pr Gr,d + Ps Gs,r + σ 2 )

higher than the transmission delay. In acoustic communication, the transmission delay is usually much higher than the processing delay. Therefore, amplifying and forwarding at the relay node will not introduce noticeable change in the delay along the sourcerelay-destination path. The signal from the direct transmission and the signal forwarded by the relay can be viewed as two paths from the multipath propagation points of view. Consequently, as long as the receiver can efficiently catch those multipath signals (for example, the RAKE receiver used in the CDMA system), the received SNR can be potentially improved. In Figure 2, we illustrates the wave propagation of the propose schemed, with a delay profile example. The wave cooperative transmission is different from multipath propagation because the paths caused by the relay node usually have much stronger signal strength than the original paths. The wave cooperative transmission is also different from the amplifyand-forward cooperative transmission in wireless networks, in which message forwarding takes place in the next time slot and does not interfere with the direct transmission. In the wave cooperative transmission, the rate can be given by: ¡ ¢ RW C = W log2 1 + ΓW C , (19)

(12)

Therefore, based on (8) and (12), after combine the signals using maximal ratio combining (MRC), we have the information rate at the output of MRC as ¡ ¢ 1 AF AF Rs,r,d = W log2 1 + ΓDT (13) s,d + Γs,r,d . 2 In the decode-and-forward (DF) cooperative transmission, the relay decodes the source information received in Phase 1 and relay to the destination in Phase 2. The destination combines the direct transmission information and the relayed information together. The achievable rate can be calculated as: DF Rs,r,d = max min{R1 , R2 } 0≤ρ≤1

where

· ¸ Ps,d Gs,r R1 = W log2 1 + (1 − ρ2 ) σ2

and

(14)

(15)

Ã

R2 = W log2

! p 2ρ Ps Gs,d Pr Gr,d Ps Gs,d Pr Gr,d 1+ + + . σ2 σ2 σ2 (16)

where ΓW C is the received SNR if the multiple paths can be resolved. Different from the rate in other cooperative transmission schemes, the rate of the waveform cooperative (WC) transmission does not have the 12 term. This is because WC does not need an additional time slot for forwarding messages. To find the close form solution for ΓW C , we need to refine the acoustic channel models to obtain phase changes from reflection and scattering. In this paper, due to the page limit, we develop a performance bound instead. We assume that the signals received from the source-to-destination path and from the relayto-destination path can be perfectly resolved. As a result, the performance of the proposed wave cooperative transmission is bounded by the sum of direct transmission SNR and relay path SNR as Ps Gs,d Pr Ps Gr,d Gs,r ΓW C ≤ + 2 . (20) 2 σ σ (Pr Gr,d + Ps Gs,r + σ 2 )

In the estimate-and-forward (EF) cooperative transmission, the relay, in Phase 2, sends an estimate of the received signal from Phase 1. The destination uses the relay’s information as the side information to decode the direct transmission in Phase 1. From [11], the achievable rate can be written as: ¡ ¢ EF EF Rs,r,d = W log2 1 + ΓDT (17) s,d + Γs,r,d , where ΓEF s,r,d =

σ 2 [Pr Gr,d

Ps Pr Gs,r Gr,d . + Ps (Gs,d + Gs,r ) + σ 2 ]

Delay profile with relay

Fig. 2: Illustration of Wave Cooperative Transmission

Using (11), the SNR of the relayed signal at the destination, is given by: ΓAF s,r,d

Multipath power

Yr Xr = |Yr |

Multipath power

where

(18)

B. Wave Cooperative Transmission Protocol The above three cooperative protocols were originally proposed for wireless networks. Based on the unique characteristics of underwater acoustic channel, we propose a new protocol named wave cooperative (WC) transmission, in which • the relay node simply amplifies the signal received from the source and forwards it to the destination immediately, instead of transmitting in the next time slot. The speed of sound (∼ 1500m/s) is much smaller than the speed of light. In radio communication, the processing delay is much

C. Implementation Concerns First, we analyze the storage concerns when using multihop relays in acoustic networks. Due to the high latency, storage required for cooperative transmission in underwater environment is much higher than that in terrestrial communications. Let S denote the propagation speed, d be the distance between the 3

Effect of Destination Location

Effect of Relay Location, Shallow Water 1.8

3.5 Direct AF DF EF WC

3

Direct AF DF EF WC

1.6 1.4

Channel Capacity

Channel Capacity

2.5

2

1.5

1.2 1 0.8 0.6

1 0.4 0.5

0.2

0 200

250

300 Destination Location

350

0

400

0

50

100

150 200 250 Relay Location

300

350

400

Fig. 3: Performance vs. Destination Location

Fig. 4: Performance vs. Relay Location, Shallow Water

transmitter and the receiver, R be the data rate, M be the number of relays, and Dprocess be the processing delay at each relay. The storage requirement at the receiver is approximately µ ¶ dR M (M − 1) Coststorage = + Dprocess · R · (21) S 2

Finally, in underwater acoustic communications, transmission is usually directional. This must be considered in the cooperative transmission scheme. Briefly speaking, the relay nodes must locate close to the direct transmission path. This will reduce the number of available relays, and also reduce the delay spread of the multipath propagation. We will investigate the effects of directional transmission in the simulation section.

For wireless communications, S = 3×105 km/s. Some typical settings are R = 250kps and d = 80m. Thus, a typical value of Coststorage is

IV. S IMULATION R ESULTS The simulation system contains two major components: acoustic field module and communication channel module. We use Bellhop Gaussian beam tracing program [15] for the acoustic field module. It computes the sound transmission loss based on the sound speed distribution of the area, bathymetry (bottom topology), source depth, source frequency and launching angles, receiver depth and distance from the source, and related media parameters. The sound speed profile used in our simulation is based on the Atlantic water sound-speed profile from the Barents Sea Polar Front experiment described in [13]. Water depth is maintained at 250m. The source emits 40kHz sound with launching angles within a 100 degree range facing the receiver. The depth of both the source and receiver increases from 0m to 250m. The program computes transmission loss at locations up to 2km away from the source. The output from the acoustic field module is then fed into the communication channel module. It evaluates the underwater acoustic channel based on the proposed methods in Section III. Here we assume that the overall power control of the source relay is 2W and the noise level is 10−5 W. In Figure 3, we show the capacity as a function of the distance from the source to the destination. Here the source depth is 1m, relay depth is 5m, and the destination receiver is at the surface. The relay is located 100m away from the source and on the line from the source to the destination. We can see that the link capacity drops as the distance increases. The AF protocol sometimes has better and sometimes has worse performance than the direction transmission, depending on the location of the destination. Compared with the direct transmission, the DF, EF, and WC protocols always have better or same performance. Among the DF, EF and WC protocols, the WC protocol has the best performance. Compared with the direct transmission, the WC protocol doubles the link quality in many cases.

M (M − 1) . (22) 2 In underwater acoustic communications, S = 1.5km/s. No research and commercial system can exceed 40 km·kbps as the maximum attainable range-rate product. Thus the typical value of Coststorage is (2.67 × 10−7 + Dprocess ) · R ·

40 M (M − 1) + Dprocess · R) · . (23) 1.5 2 From (22) and (23), we can see that the processing delay dominates the storage cost in wireless communications, but the propagation delay dominates the storage cost in underwater acoustic communications. In wireless communications, even if the processing delay is at the order of ms, the storage requirement is 0.25M (M − 1)/2kb, which is very small. But in underwater acoustic communications, if we neglect the processing delay in (23), the storage requirement is roughly (

M (M − 1) · 27kb. (24) 2 From (24), we can see that the storage cost for cooperative transmission in underwater acoustic communications is not negligible. However, it is tolerable as long as the M value is not too large. In other words, for underwater acoustic communications, the number of relays needs to be small. Second, for underwater acoustic networks, one major concern is the high energy consumption in acoustic transmission. In cooperative transmission, with the same transmission power, the received SNR can be greatly improved. Therefore, with the same reliability requirement, the transmission power can be greatly reduced. This is the major advantage of utilizing cooperative transmission in underwater networks. 4

Effect of Relay Location, Deep Water

Effect of Relay Depth

3

1.8 Direct AF DF EF WC

1.4

2

Channel Capacity

Channel Capacity

2.5

Direct AF DF EF WC

1.6

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1.2 1 0.8 0.6

0.5 0.4 0

0

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100

150 200 250 Relay Location

300

350

0.2

400

0

50

100 150 Relay Depth

200

250

Fig. 5: Performance vs. Relay Location, Sea Bottom

Fig. 6: Performance vs. Relay Depth

In Figure 4, we show the link capacity as a function of relay location near the surface at 1m depth. Here the source, relay, and destination have the same depth. The destination is located 400m away from the source, and the relay locates at 10m ∼ 390m along the line from the source to the destination. We can see that the AF and EF protocols have similar performances, except that the DF protocol has less link capacity than the direct transmission when the relay is far away from the source. This is because the decoding of the source’ information at the relay can contain errors. As a result, the link capacity drops if the destination combines the source and relay transmission. The proposed WC protocol always has the best performance. In Figure 5, we show the performances for nodes located near the sea floor, where the source, relay, and destination are 240m deep. We can see that the performance of direct transmission is poor and the relay can significantly improve the performance for all protocols. However, similar to Figure 3 and 4, the performance improvement has the breathing effect. In other words, the cooperative transmission can improve performance only when the relays are at certain locations. This may be due to the directional transmission of acoustic signals, and the bouncing of signals from the surface and bottom. In Figure 6, we show the effects of relay depth. Here the source is 1m deep and the destination is 400m away on the surface. The relay is located at 200m away and changes its depth. We can see that the relay has the best performance when it is 10m deep. This is because the relay can get the signal in time and can avoid severe multipath effects. When the relay is about half of the sea depth, the performance is also good. This is because the relay is on the path of multipath propagation. When the relay is too deep, the performance drops.

the line-of-sigh between the source and the destination. Second, the multipath effect of acoustic signal causes the breathing effect. Third, the storage overhead of cooperative transmission in underwater environment is much higher than that in wireless communications. Finally, the newly proposed wave cooperative transmission scheme outperforms the existing cooperative transmission schemes designed for wireless communications. R EFERENCES [1] E. M. Sozer, M. Stojanovic, and J. G. Proakis, “Underwater acoustic networks”, IEEE Journal of Oceanic Engineering, vol.25, no.1, p.p.72-83, Januray 2000. [2] J. Preisig, “Acoustic propagation considerations for underwater acoustic communications network development”, in Proceedings of the 1st ACM international workshop on Underwater networks, p.p.1-5, September 2006. [3] P. C. Etter, Underwater acoustic modeling and simulation, 3rd ed., Spon Press, Taylor & Francis Group, 2003. [4] R. J. Urick, Principles of underwater sound, 3rd ed., McGraw-Hill, Inc, 1983. [5] D. B. Kilfoyle and A. B. Baggeroer, “The state of the art in underwater acoustic telemetry,” IEEE Journal of Oceanic Engineering, vol.25, no. 1, pp.4-27, January 2000. [6] A. K. Morozov and J. C. Preisig, “Underwater acoustic communications with multi-carrier modulation”, OCEANS 2006, p.p.1-6, September 2006. [7] M. Stojanovic and L. Freitag, “Multichannel detection for wideband underwater acoustic CDMA communications”, IEEE Journal of Oceanic Engineering, vol.31, no.3, p.p.685-695, July 2006. [8] D. B. Kilfoyle, J. C. Preisig, and A. B. Baggeroer, “Spatial modulation experiments in the underwater acoustic channel”, IEEE Journal of Oceanic Engineering, vol.30, no.2, p.p.406-415, April 2005. [9] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity, Part I: System description,” IEEE Transactions on Communications, vol.51, no.11, pp.1927-1938, November 2003. [10] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: efficient protocols and outage behavior,” IEEE Trans. on Information Theory, vol.50, no.12, pp.3062-3080, December 2004. [11] M. A. Khojastepour, A. Sabharwal and B. Aazhang, “On the capacity of ‘cheap’ relay networks,” in Proc. 37th Annual Conference on Information Sciences and Systems, Baltimore, MD, March 2003. [12] Z. Han and H. V. Poor, “Coalition game with cooperative transmission: a cure for the curse of boundary nodes in selfish packet-forwarding wireless networks”, in Proceedings of WiOpt07, Limassol, Cyprus, April 2007. [13] G. Jin, J. F. Lynch, C. S. Chiu and J. H. Miller, “A theoretical and simulation study of acoustic normal mode coupling effects due to the Barents Sea Polar Front, with applications to acoustic tomography and matched-field processing,” Journal of the Acoustical Society of America, vol. 100, no. 1, pp.193-205, July 1996. guides speed of sound in sea[14] “Technical water,” the National Physical Laboratory, http://www.npl.co.uk/acoustics/techguides/soundseawater/content.html. [15] Available at ONR Ocean Acoustics Library, http://oalib.hlsresearch.com/.

V. C ONCLUSIONS Cooperative transmission is a new communication paradigm in wireless communications. In this paper, we investigated the effects of cooperative transmission on underwater acoustic communications. We studied the differences between direct transmission and cooperative transmission, and proposed a new cooperative transmission scheme for the underwater environment. Our study has shown several unique features of the cooperative transmission in underwater acoustic environment. First, when the acoustic signal transmission is directional, the relay must locate close to 5